The fur-bearing trout, also known as the beaver trout, is a trout that possesses a thick coat of fur to keep it warm in the extremely cold northern waters it lives in. It was obviously since fish do not typically sprout fur and they are already adapt to the waters they live in.
According to the legend, it was first encountered by Europeans who settled in Canada and talked about many furred animals and fish in the lands and was asked to specify the fur fish and so it became to be the fur bearing fish. Now they are many mounted up on walls all through the Great Lakes of North America as a little tribute to that. There are some cases where fish will seem to have fur, but that due to a disease called saprolegnia which causes what looks like little tufts of fur.